\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,x+F \left ( y \left ( x \right ) -{x}^{2} \right ) =0} \]
Mathematica: cpu = 16.413084 (sec), leaf count = 97 \[ \text {Solve}\left [\int _1^{y(x)} -\frac {F\left (K[2]-x^2\right ) \int _1^x -\frac {2 K[1] F'\left (K[2]-K[1]^2\right )}{F\left (K[2]-K[1]^2\right )^2} \, dK[1]+1}{F\left (K[2]-x^2\right )} \, dK[2]+\int _1^x \left (\frac {2 K[1]}{F\left (y(x)-K[1]^2\right )}+1\right ) \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 22 \[ \left \{ y \left ( x \right ) ={x}^{2}+{\it RootOf} \left ( -x+\int ^{{ \it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a }}+{\it \_C1} \right ) \right \} \]